Exercises: Linear functions and line equations

Coordinate system

1.

2.

Consider $A(40|220)$ and $B(100|250)$.

Choose ... from A

and ... from B

$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{y_2-y_1}{x_2-x_1}=\frac{250-220}{100-40}=\frac{30}{60}=0.5$

Since the points $A$-$D$ all lie on a common line, it is sufficient to select only two points (for example $A$ and $B$). With their help you determine the slope of the line. To do this, subtract the $y$-coordinate of point $A$ from the $y$-coordinate of point $B$, and the $x$-coordinate of point $A$ from the $x$-coordinate of point $B$.

Then determine the $y$-axis intercept by inserting a point on the straight line (for example C) into the straight line equation $y=mx+t$ and solving for $t$.

Insert point $C$ into the line equation $y=mx+t$ together with the previously calculated $m=0.5$:

With this we have determined both $m$ and $t$, so that our line equation is:

$y=0.5\cdot x+200$

3.

Insert any three $x$-values into the line equation to get the respective $y$-value, e.g. $x_1=0$, $x_2=-100$ and $x_3=300$.

This gives us the following three points $D$, $E$ and $F$:

$D(0|200),E(-100|150)$ and $F(300|350)$